A041544 Numerators of continued fraction convergents to sqrt(290).

17, 579, 19703, 670481, 22816057, 776416419, 26420974303, 899089542721, 30595465426817, 1041144914054499, 35429522543279783, 1205644911385567121, 41027356509652561897, 1396135766239572671619, 47509643408655123396943, 1616724011660513768167681

Offset

0,1

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..200

Tanya Khovanova, Recursive Sequences

Index entries for linear recurrences with constant coefficients, signature (34,1).

Formula

a(n) = 34*a(n-1)+a(n-2) for n>1, a(0)=17, a(1)=579. G.f.: (17+x)/(1-34*x-x^2). [Philippe Deléham, Nov 23 2008]

Maple

numtheory:-cfrac(sqrt(290), 30, 'convergents'):
map(numer, convergents[1..-2]); # Robert Israel, Jun 22 2015

Mathematica

Numerator[Convergents[Sqrt[290], 30]] (* Vincenzo Librandi, Nov 04 2013 *)

Crossrefs

Cf. A041545.

Sequence in context: A249862 A056771 A041547 * A202407 A009709 A162490

Adjacent sequences: A041541 A041542 A041543 * A041545 A041546 A041547

Keyword

nonn,cofr,frac,easy

Author

N. J. A. Sloane.

Extensions

Additional term from Colin Barker, Nov 08 2013

Status

approved